Viscoelastic dampers are now among some of the preferred energy dissipation devices used for passive seismicresponse control.To evaluate the performance of structures installed with viscoelastic dampers,different analytical modelshave been used to characterize their dynamic force deformation characteristics.The fractional derivative models have receivedfavorable attention as they can capture the frequency dependence of the material stiffness and damping properties observed inthe tests very well.However,accurate analytical procedures are needed to calculate the response of structures with suchdamper models.This paper presents a modal analysis approach,similar to that used for the analysis of linear systems,forsolving the equations of inotion with fractional derivative terms for arbitrary forcing functions such as those caused byearthquake induced ground motions.The uncoupled modal equations still have fractional derivatives,but can be solved bynumerical or analytical procedures.Both numerical and analytical procedures are formulated.These procedures are thenused to calculate the dynamic response of a multi-degree of fleedom shear beam structure excited by ground motions.Numerical results demonstrating the response reducing effect of viscoelastic dampers are also presented. Viscoelastic dampers are now among some of the preferred energy dissipation devices used for passive seismicresponse control. To evaluate the performance of structures installed with viscoelastic dampers, different analytical modelshave been used to characterize their dynamic force deformation characteristics. Fractional derivative models have receivedfavorable attention as they can capture the frequency dependence of the material stiffness and damping properties observed inthe tests very well. However, accurate analytical procedures are needed to calculate the response of structures with such damper models. This paper presents a modal analysis approach, similar to that used for the the analysis of linear systems, forsolving the equations of inotion with fractional derivative terms for arbitrary forcing functions such as those caused byearthquake induced ground motions. The uncoupled modal equations still have fractional derivatives, but can be solved byumerical or analytical procedures.Both num erical and analytical procedures are then used to calculate the dynamic response of a multi-degree of fleed shear beam structure excited by ground motions. Numerical results demonstrating the response reducing effect of viscoelastic dampers are also presented.